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Jacel Delgadillo said she has tried a host of treatments to help her 2-year-old son, Bruno, cope with severe seizures triggered by a rare form of epilepsy, from a special diet to more than a dozen medications. But nothing has worked.

Now she hopes a legislative proposal in Florida will provide a new option: a marijuana extract called cannabidiol, or CBD, that anecdotal evidence suggests is effective in treating the disorder.

The substance, which doesn't produce a high and can be taken orally in an oil form, has been embraced by parents whose children, like Bruno, suffer from Dravet syndrome, which occurs in about one of every 30,000 births. The condition begins in infancy and can cause hundreds of seizures a day, developmental delays and even death.

"I'm praying that it becomes available here," said Ms. Delgadillo, a 37-year-old single mother of two in Miami. "It's our last option."

Lawmakers here and in a handful of other states are weighing measures to effectively legalize marijuana derivatives that are high in CBD and low in tetrahydrocannabinol, or THC, the psychoactive compound in pot. Among them are Republicans who otherwise strongly oppose authorizing the use of marijuana for medicinal purposes.

"I'm a converted zealot," said Rep. Matt Gaetz, the Republican chairman of the criminal justice subcommittee in the Florida House. He said he originally was against legalizing CBD because he thought it could open the way to broader use of medical marijuana. But after hearing the accounts of desperate families, he said he changed his mind.

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